Moment of Inertia
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365861 One quarter of the plate is cut from a square plate as shown in the figure. If \(M'\) is the mass of the plate and \(\ell\) is the length of each side, then the moment of inertia of the plate about an axis passing through \(O'\) and perpendicular to the plate is
supporting img

1 \(M \ell^{2} / 8\)
2 \(3 M \ell^{2} / 4\)
3 \(M \ell^{2} / 3\)
4 \(3 M \ell^{2}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365862 From a circular ring of mass ' \(M\) ' and radius ' \(R\) ' an arc corresponding to a \(90^{\circ}\) sector is removed. The moment of inertia of the remaining part of the ring about an axis passing through the centre of the ring and perpendicular to the plane of the ring is \('K'\) times \('M{R^2}\). Then the value of \('K'\) is

1 \(\dfrac{7}{8}\)
2 \(\dfrac{1}{4}\)
3 \(\dfrac{1}{8}\)
4 \(\dfrac{3}{4}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365863 The ratio of the radius of gyration of a thin unifrom disc about an axis passing through its centre and normal to its plane to the radius of gyration of the disc about its diameter is

1 \(\sqrt{2}: 1\)
2 \(4: 1\)
3 \(1: \sqrt{2}\)
4 \(2: 1\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365864 A ring of mass \(m\) and radius \(r\) is melted and then moulded into a sphere. The moment of inertia of the sphere will be

1 More than that of the ring
2 Less than that of the ring
3 Equal to that of the ring
4 Exactly one quarter that of the ring
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365865 Two discs have same mass and thickness. Their materials have densities \(d_{1}\) and \(d_{2}\). The ratio of their moments of inertia about central axis will be

1 \(1: d_{1} d_{2}\)
2 \(d_{1}: d_{2}\)
3 \(d_{2}: d_{1}\)
4 \(d_{1} d_{2}: 1\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365861 One quarter of the plate is cut from a square plate as shown in the figure. If \(M'\) is the mass of the plate and \(\ell\) is the length of each side, then the moment of inertia of the plate about an axis passing through \(O'\) and perpendicular to the plate is
supporting img

1 \(M \ell^{2} / 8\)
2 \(3 M \ell^{2} / 4\)
3 \(M \ell^{2} / 3\)
4 \(3 M \ell^{2}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365862 From a circular ring of mass ' \(M\) ' and radius ' \(R\) ' an arc corresponding to a \(90^{\circ}\) sector is removed. The moment of inertia of the remaining part of the ring about an axis passing through the centre of the ring and perpendicular to the plane of the ring is \('K'\) times \('M{R^2}\). Then the value of \('K'\) is

1 \(\dfrac{7}{8}\)
2 \(\dfrac{1}{4}\)
3 \(\dfrac{1}{8}\)
4 \(\dfrac{3}{4}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365863 The ratio of the radius of gyration of a thin unifrom disc about an axis passing through its centre and normal to its plane to the radius of gyration of the disc about its diameter is

1 \(\sqrt{2}: 1\)
2 \(4: 1\)
3 \(1: \sqrt{2}\)
4 \(2: 1\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365864 A ring of mass \(m\) and radius \(r\) is melted and then moulded into a sphere. The moment of inertia of the sphere will be

1 More than that of the ring
2 Less than that of the ring
3 Equal to that of the ring
4 Exactly one quarter that of the ring
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365865 Two discs have same mass and thickness. Their materials have densities \(d_{1}\) and \(d_{2}\). The ratio of their moments of inertia about central axis will be

1 \(1: d_{1} d_{2}\)
2 \(d_{1}: d_{2}\)
3 \(d_{2}: d_{1}\)
4 \(d_{1} d_{2}: 1\)
NEET Test Series from KOTA - 10 Papers In MS WORD WhatsApp Here
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365861 One quarter of the plate is cut from a square plate as shown in the figure. If \(M'\) is the mass of the plate and \(\ell\) is the length of each side, then the moment of inertia of the plate about an axis passing through \(O'\) and perpendicular to the plate is
supporting img

1 \(M \ell^{2} / 8\)
2 \(3 M \ell^{2} / 4\)
3 \(M \ell^{2} / 3\)
4 \(3 M \ell^{2}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365862 From a circular ring of mass ' \(M\) ' and radius ' \(R\) ' an arc corresponding to a \(90^{\circ}\) sector is removed. The moment of inertia of the remaining part of the ring about an axis passing through the centre of the ring and perpendicular to the plane of the ring is \('K'\) times \('M{R^2}\). Then the value of \('K'\) is

1 \(\dfrac{7}{8}\)
2 \(\dfrac{1}{4}\)
3 \(\dfrac{1}{8}\)
4 \(\dfrac{3}{4}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365863 The ratio of the radius of gyration of a thin unifrom disc about an axis passing through its centre and normal to its plane to the radius of gyration of the disc about its diameter is

1 \(\sqrt{2}: 1\)
2 \(4: 1\)
3 \(1: \sqrt{2}\)
4 \(2: 1\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365864 A ring of mass \(m\) and radius \(r\) is melted and then moulded into a sphere. The moment of inertia of the sphere will be

1 More than that of the ring
2 Less than that of the ring
3 Equal to that of the ring
4 Exactly one quarter that of the ring
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365865 Two discs have same mass and thickness. Their materials have densities \(d_{1}\) and \(d_{2}\). The ratio of their moments of inertia about central axis will be

1 \(1: d_{1} d_{2}\)
2 \(d_{1}: d_{2}\)
3 \(d_{2}: d_{1}\)
4 \(d_{1} d_{2}: 1\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365861 One quarter of the plate is cut from a square plate as shown in the figure. If \(M'\) is the mass of the plate and \(\ell\) is the length of each side, then the moment of inertia of the plate about an axis passing through \(O'\) and perpendicular to the plate is
supporting img

1 \(M \ell^{2} / 8\)
2 \(3 M \ell^{2} / 4\)
3 \(M \ell^{2} / 3\)
4 \(3 M \ell^{2}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365862 From a circular ring of mass ' \(M\) ' and radius ' \(R\) ' an arc corresponding to a \(90^{\circ}\) sector is removed. The moment of inertia of the remaining part of the ring about an axis passing through the centre of the ring and perpendicular to the plane of the ring is \('K'\) times \('M{R^2}\). Then the value of \('K'\) is

1 \(\dfrac{7}{8}\)
2 \(\dfrac{1}{4}\)
3 \(\dfrac{1}{8}\)
4 \(\dfrac{3}{4}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365863 The ratio of the radius of gyration of a thin unifrom disc about an axis passing through its centre and normal to its plane to the radius of gyration of the disc about its diameter is

1 \(\sqrt{2}: 1\)
2 \(4: 1\)
3 \(1: \sqrt{2}\)
4 \(2: 1\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365864 A ring of mass \(m\) and radius \(r\) is melted and then moulded into a sphere. The moment of inertia of the sphere will be

1 More than that of the ring
2 Less than that of the ring
3 Equal to that of the ring
4 Exactly one quarter that of the ring
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365865 Two discs have same mass and thickness. Their materials have densities \(d_{1}\) and \(d_{2}\). The ratio of their moments of inertia about central axis will be

1 \(1: d_{1} d_{2}\)
2 \(d_{1}: d_{2}\)
3 \(d_{2}: d_{1}\)
4 \(d_{1} d_{2}: 1\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365861 One quarter of the plate is cut from a square plate as shown in the figure. If \(M'\) is the mass of the plate and \(\ell\) is the length of each side, then the moment of inertia of the plate about an axis passing through \(O'\) and perpendicular to the plate is
supporting img

1 \(M \ell^{2} / 8\)
2 \(3 M \ell^{2} / 4\)
3 \(M \ell^{2} / 3\)
4 \(3 M \ell^{2}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365862 From a circular ring of mass ' \(M\) ' and radius ' \(R\) ' an arc corresponding to a \(90^{\circ}\) sector is removed. The moment of inertia of the remaining part of the ring about an axis passing through the centre of the ring and perpendicular to the plane of the ring is \('K'\) times \('M{R^2}\). Then the value of \('K'\) is

1 \(\dfrac{7}{8}\)
2 \(\dfrac{1}{4}\)
3 \(\dfrac{1}{8}\)
4 \(\dfrac{3}{4}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365863 The ratio of the radius of gyration of a thin unifrom disc about an axis passing through its centre and normal to its plane to the radius of gyration of the disc about its diameter is

1 \(\sqrt{2}: 1\)
2 \(4: 1\)
3 \(1: \sqrt{2}\)
4 \(2: 1\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365864 A ring of mass \(m\) and radius \(r\) is melted and then moulded into a sphere. The moment of inertia of the sphere will be

1 More than that of the ring
2 Less than that of the ring
3 Equal to that of the ring
4 Exactly one quarter that of the ring
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365865 Two discs have same mass and thickness. Their materials have densities \(d_{1}\) and \(d_{2}\). The ratio of their moments of inertia about central axis will be

1 \(1: d_{1} d_{2}\)
2 \(d_{1}: d_{2}\)
3 \(d_{2}: d_{1}\)
4 \(d_{1} d_{2}: 1\)